DOI 10.1393/ncc/i2005-10211-5
Study of the response of a single photon counting system
in various experimental conditions for low-energy
radiological applications
(∗)
M. G. Bisogni, E. Cicalini, A. Del Guerra, P. Delogu, C. Carpentieri, M. E. Fantacci, D. Panetta,
M. Quattrocchi, V. Rosso(∗∗) and A. Stefanini
Dipartimento di Fisica “E. Fermi”, Universit`a di Pisa - Pisa, Italy
INFN, Sezione di Pisa - Pisa, Italy
(ricevuto il 14 Dicembre 2005; revisionato il 28 Marzo 2006; approvato il 28 Marzo 2006; pub-blicato online il 10 Luglio 2006)
Summary. — In low-energy radiological applications the capability to have
repro-ducible image uniformity and good detection efficiency are relevant issues. A single photon counting system based on a 700µm thick silicon pixel detector, to ensure a good detection efficiency, and connected to the Medipix2 read-out chip is a good candidate to realize a low-noise detection system with a stable response. We present the experimental results obtained with this system. The performaces obtained with a variable thickness phantom are also reported.
PACS87.59.Hp – Digital radiography. PACS87.58.Mj – Digital imaging.
Introduction
Due to their good performances, to the possibility of implementing computer image processing techniques, digital archiving and transmission of images, digital systems are rapidly spreading over all medical radiographic fields [1]. Often these digital systems have the read-out based on charge integrating electronics, but also single photon counting systems have been commercialized [2-4] and furthermore, new single photon counting systems are under development [5-8].
A point of merit for these radiographic systems is the capability to display small differences in tissues attenuation: this is only possible with a reproducible and uniform system response [9]. We describe the experimental results obtained using a single photon
(∗) The authors of this paper have agreed to not receive the proofs for correction. (∗∗) E-mail: valeria.rosso@pi.infn.it.
c
counting system in terms of image uniformity in various experimental conditions for low-energy applications.
1. – Experimental apparatus
Our imaging system is based on the Medipix2 read-out chip [10], bump-bonded to a 700µm thick silicon pixel detector: the evaluated detection efficiency is 73% for a 30 kVp X-ray beam, taking into account the 10 keV experimental detection energy threshold [11]. The read-out chip is a matrix of 256× 256 cells, 55 µm pitch, each cell featuring a low-noise preamplifier, two pulse height discriminators and a 13 bit pseudo-random counter for a wide dynamic range. The two discriminators are identical and independent; the difference between the two energy levels defines the energy window into which the energy deposited by the incident photon has to fall in order to increase the counter. The system can also work in single discrimination mode and the counter is incremented when the energy deposited by the incident photon exceeds the low threshold level. We have worked in single discrimination mode.
The X-ray source used is a micro-focus tube with W anode, 30µm focus size and with a 150µm thick Be window: for some measurements a 1 mm thick Al filter was added.
The anode voltage (30 kVp) and the current (150µA) were kept constant and the detection threshold used during all acquisitions was fixed at a value of 10 keV, the lowest possible value for the used read-out chip. The calibration of the threshold value was ob-tained using different W spectra endpoints and verifying the obob-tained calibration straight line with a109Cd source.
To detect low-contrast objects, it is necessary to reduce the structured noise on the detector, limiting the difference in the response of the pixels. This requires to have a very narrow distribution of the response of the 65536 pixels for a flat irradiation field. To achieve this result, it is necessary, first, to optimize the threshold value for each pixel with a well-established procedure (applying a global threshold value to the matrix and then regulating, pixel by pixel, a fine threshold adjustment [12]) and then to equalize each image with a high statistical flat-field image. The procedure described above is effective only if the system response is reproducible.
In this study we have investigated how the equalization process affects the response of the system using different X-rays spectra and phantoms of various thicknesses and composition as described in the following.
2. – Discussion and results
2.1.Uniform thickness phantoms. – To investigate how the equalization process, that needs the use of a high statistical flat-field image, is affected by the flat-field experimen-tal acquisition condition, various sets of measurements were performed with different homogeneous phantoms (wax, lucite and air) interposed between the X-ray source and the detection system. We started working with fixed thickness phantoms of different materials: wax, lucite and air. The distance between the detector and the beam focus was always 40 cm and the phantom was positioned in the middle.
The thickness of the homogeneous wax phantom was 2.2 cm, that of the homogeneous lucite phantom was 2.0 cm and that of the air phantom was 40 cm (the distance between the X-ray source and our detection system).
A significant number of images has been taken for each of the three materials: each image has the same mean photon counts and since the attenuation coefficient varies
2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 0 500 1000 1500 2000 2500 numb er of pi xe ls
Detected photon s per pixel
Wax im a ge equalized wi th Wa x
Lu ci te Ai r
Fig. 1. – Counts distributions of the wax attenuator image equalized with different flat fields when the incident X-ray beam was unfiltered.
among the materials, a fixed photon number was obtained by keeping constant the anode voltage and the current, and varying the exposition time. One image for each group was then chosen at random and equalized, in sequence, using the remaining images of that group: each group of images create a flat field. The flat fields were acquired with 2.2 cm wax plus 37.8 cm of air, or 2.0 cm lucite plus 38 cm of air or 40 cm of air. The counts distributions on the equalized images were then compared in terms of standard deviation. As an example, in fig. 1 is reported the count distribution for the image of the wax phantom equalized using the above-mentioned three different high statistical flat-field images (wax, lucite and air). In this case the incident spectrum was unfiltered.
The narrowest counts distribution is obtained by equalizing the wax phantom image with a flat field acquired with the wax attenuator, while the wider distribution is obtained equalizing the wax attenuator image with the flat field obtained using air as attenuator. The calculated standard deviations divided by the mean photon counts are reported in the first column of table I.
When the Al filter is used, the previous differences in the counts distributions (see
TableI. – Standard deviation divided by the mean photon count on the equalized images with
unfiltered X-ray beam: all the images have the same mean photon count.
Image Wax Lucite Air
Flat field
Wax 0.022 0.024 0.046
Lucite 0.024 0.021 0.055
2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 0 500 1000 1500 2000 2500 Wax im a ge equalized wi th Wa x Lu ci te Ai r Co un ts Photons number
Fig. 2. – Counts distributions of the wax attenuator image equalized with different flat fields when the incident X-ray beam was filtered with 1 mm thick Al.
fig. 1) disappear: the counts distributions are now well superimposed and they have almost the same standard deviations as reported in fig. 2 and in the first column of table II, where the calculated standard deviations divided by the mean photon counts are reported.
The same study was performed for all the possible combinations of the three materials images and flat fields: the results are summarized in table I for the unfiltered X-ray beam, and in table II for the filtered X-ray beam. Once again for the unfiltered case, the narrowest values were obtained when the image and the used flat field were acquired using the same material as phantom and as attenuator: the diagonal terms of table I. Looking at the off-diagonal terms of table I, we observe a large variation for the standard deviation values: in some case the off-diagonal term value is more than twice the diagonal values.
The large variation of the standard deviation values disappears using a filtered X-ray beam. Since the mean photon number is the same for each image, this is due to the fact that the image and the corresponding flat field were acquired with almost the same photon energy distribution.
TableII. – Standard deviation divided by the mean photon count on the equalized images with
filtered X-ray beam: all the images have the same mean photon count.
Image Wax Lucite Air
Flat field
Wax 0.021 0.022 0.022
Lucite 0.022 0.022 0.022
a)
10 15 20 25 30 100 1000 10 000 100 000 1000 00030 kVp spectra attenuated by: 40 cmAi r 37.8cm Ai r + 2.2 cm Wa x 38.0cm Ai r + 2.0 cm Lu cite Energy(keV) b) 100 1000 10 000 100 000 1000 000 10 15 20 25 30 Energy(keV) 30 kVp spectra attenuated by:
40 cmAi r 37.8cm Ai r + 2.2 cm Wa x 38.0cm Ai r + 2.0 cm Lu cite
Fig. 3. – Simulated spectra for unfiltered a) and filtered b) X-ray beam. The 10 keV applied threshold is also reported.
The above conclusion is well demonstrated if we take a look at the simulated spec-tra [11] impinging on the detection system: the simulations are reported in fig. 3a) and b). In fig. 3a) is reported the fluency for the unfiltered case for the three different at-tenuators: the mean energy ranges from 15.6 keV for the air attenuator simulation to 21.1 keV for the lucite attenuator simulation, taking into account the 10 keV experimen-tal detection energy threshold. In fig. 3b) is reported the fluency for the filtered case in the same condition as above. In this case the mean energy ranges from 21.9 keV for the air attenuator simulation to 22.7 keV for the lucite attenuator simulation: a very small variation with respect to the unfiltered case.
2.2.Variable thickness phantom. – To investigate how the equalization process affects a variable thickness phantom image, a five-step wax stair was used and different flat fields were acquired by varying the thickness of the attenuator: for this study only the wax attenuators were used.
The wax stairs height varies from 3.5 mm, step no. 1, to 18 mm, step no. 5, each step is about 1 cm wide; its center was positioned about in the middle between the detector and the beam focus. The distance between the detector and the beam focus was again 40 cm.
The image of all steps (fig. 4) has been obtained by translating the detector in seven different positions of the irradiation field.
These images have been equalized using different flat fields acquired with five different wax thicknesses: the thickness of each attenuator was chosen so as to be closest to a wax stairs step height. The standard deviation was evaluated on an area of 50× 50 pixels
Fig. 4. – Image of the wax stairs with 5 steps acquired at 30 kVp, 150µA and 1 mm thick Al filter. The darkest zone, on the right, corresponds to the 18 mm step, while the white zone, on the left, corresponds to a zone outside the wax.
1 2 3 4 5 15 20 25 30 35 40 3.05 mm 6.20 mm 12 .10 mm 15.35 mm 18.40 mm Poiss on approx. standard devia ti on step #
Fig. 5. – Unfiltered X-ray beam case: the behavior of the standard deviation as a function of the wax thickness used for the equalization process. The standard deviation value expected in Poisson approximation is also reported.
for each step as a function of the wax thickness used as attenuator for the flat-field acquisition. This study was carried out for the unfiltered and for the filtered X-ray beam.
When the unfiltered beam is used, the narrowest standard deviation is obtained when the wax attenuator, used for the flat-field acquisition, has the thickness value closest to the step height. If the difference between the step height and the used wax attenuator is increased, the standard deviation also increases: the spread of the standard devia-tions for the 5 attenuator thicknesses decreases as the height of the step increases, as
1 2 3 4 5 26 28 30 32 34 36 38 40 Air 3.05 mm 6.20 mm 12.10 mm 15.35 mm 18.40 mm Poisson approx. standard devia ti on step #
Fig. 6. – Filtered X-ray beam case: the behavior of the standard deviation as a function of the wax thickness used for the equalization process. The standard deviation value expected in Poisson approximation is reported.
reported in fig. 5.
With filtered beam, the equalization process becomes almost independent of the steps height. In fig. 6 there are reported the standard deviations of each step image equalized with the different wax attenuators. Inside each step the differences among the standard deviations are really small indicating that the energy spectra are very similar. This is confirmed by the fact that even using air, as attenuator, the corresponding standard deviation is very close to the other values.
3. – Conclusions
A study of the response of a single photon counting system has been performed in various experimental conditions. The attention was devoted to the capability obtaining a uniform image in correspondence to a uniform phantom. It has been demonstrated that a good image equalization has been obtained by using flat fields acquired with a similar photon energy spectrum. This was well put into evidence by using filtered and unfiltered X-rays beams. However, using filtered beams the energy dependence almost disappears, thus suggesting the possibility to use the same flat field for a variable thickness phantom, that is the most common experimental condition.
The obtained standard deviations are very close to the expected values calculated with the Poisson approximation, making us confident of the capability of this single photon counting digital system to display small differences in tissues attenuation for future applications in Computed Tomography.
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